STABILITY OF THE STOCHASTIC HEAT EQUATION IN L1([0,1])

被引：2

作者：

Fournier, Nicolas ^{[1
]}

Printems, Jacques ^{[1
]}

机构：

[1] Univ Paris Est, CNRS, UMR 8050, LAMA, F-94010 Creteil, France

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2011年 / 16卷

关键词：

Stochastic partial differential equations; White noise; Invariant distributions; Asymptotic confluence; Stability; Long time behavior; Existence; PARTIAL-DIFFERENTIAL EQUATIONS; DRIVEN PARABOLIC SPDES; WHITE-NOISE;

D O I：

10.1214/ECP.v16-1636

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider the white-noise driven stochastic heat equation on [0, infinity) x [0, 1] with Lipschitz-continuous drift and diffusion coefficients. We derive an inequality for the L-1([0, 1])-norm of the difference between two solutions. Using some martingale arguments, we show that this inequality provides some estimates which allow us to study the stability of the solution with respect the initial condition, the uniqueness of the possible invariant distribution and the asymptotic confluence of solutions.

引用

页码：337 / 352

页数：16

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